Capital calculation methods

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Looking for something in between nested stochastic and the standard formula • What is the most annoying about the nested stochastic method • That you have to calculate many inner scenarios for each outer scenario – i.e. calculating the value of liabilities in each scenario is complex • Can we go around this somehow • Instead of doing the full liability valuation run in each outer scenario let’s do something more simple – proxy methods to liability valuation • Let’s calculate the full valuation of the liabilities in a few outer scenarios and interpolate the behaviour = Curve Fitting • Let’s calculate only a few random inner scenarios for each outer scenario = least squares Monte Carlo (LSMC) • Let’s replace the liabilities by an easy to value combination of assets, which produce the same cash-flows = Replicating Portfolios • The rest stays the same as in nested stochastic • We have marginal distributions of risk factors and dependencies based on copulas • We create a large set (e.g. 100 000) of outer scenarios (vectors of risk factors) • In each of the scenarios we value the liability by use of the proxy method • We get a distribution of own funds and from that we find the quantile 12 Capital calculation methods © 2012 Deloitte Česká republika
Curve fitting - principles • The stochastic liability model (e.g. Prophet ALS) can be viewed as a black box which has as inputs the value of the risk factors (outer scenario) and as an output the value of the liabilities in this scenario • The idea of curve fitting is to replace the slow black box (e.g. Prophet model) by a fitted function of the risk factors – the loss function • In that case it’s enough to run the liability model only in a few risk factor scenarios and interpolate between them • Then whatever combination of risk factors is brought (outer scenario) the liability valuation consists only of evaluating the interpolated function in the given points – this is very quick and easy 13 Capital calculation methods © 2012 Deloitte Česká republika
Page 1 and 2: Metody pro výpočet kapitálu Inte
Page 3 and 4: Solvency II Requirements • Solven
Page 5 and 6: Joint distribution of risk factors
Page 7 and 8: Own funds impact - Asset and Liabil
Page 9 and 10: The standard formula - implicit sim
Page 11: Standard formula - advantages and d
Page 15 and 16: Curve fitting - advantages and disa
Page 17 and 18: Least squares Monte Carlo - practic
Page 19 and 20: Replicating portfolios - principles
Page 21 and 22: Replicating portfolios - practice
Page 23 and 24: How to use this • Directly - impl
Page 25 and 26: Contact Petr Bednařík Manager, Cz

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